Cycles Render: Light reflections black in render
The mistake is in your shader. You are mixing two glass shaders depending on the viewing angle. This causes the physically incorrect resut. Strip out the dark glass, the mix shader and the layer weight node and everything renders fine.



Edit

There are comments mentioning poor rendering optimization, so I took a closer look at your file and reduced the rendertime from estimated 1,5 h to just over 14 minutes at 5760 x 3240 pixel.

The changes:


replaced all mesh lights with area and point lamps, they are much less expensive to compute (less noise)
deactivated the direct and indirect clamping. This reveals, that your lights are way too bright and cause the reflections to blow out. reduced all lamps so the reflection values stay below 1.
deactivated "progressive refine", this slows down your final render significantly
raised tile size to 1024 x 1024 pixel (this might be GPU-dependent and slower on your machine, you might leave it at 512 px².
reduced samples to 512. Without the mesh lights we can get away with less samples
deactivated denoising, it is not necessary here, imho. The image is virtually noise free after 512 samples.


The optimized .blend: